On tame embeddings of solenoids into 3-space

Fuente: arXiv
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Main Authors: Jiang, Boju, Wang, Shicheng, Zheng, Hao, Zhou, Qing
Format: Preprint
Published: 2006
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author Jiang, Boju
Wang, Shicheng
Zheng, Hao
Zhou, Qing
author_facet Jiang, Boju
Wang, Shicheng
Zheng, Hao
Zhou, Qing
contents Solenoids are ``inverse limits'' of the circle, and the classical knot theory is the theory of tame embeddings of the circle into the 3-space. We give some general study, including certain classification results, of tame embeddings of solenoids into the 3-space as the ``inverse limits'' of the tame embeddings of the circle. Some applications are discussed. In particular, there are ``tamely'' embedded solenoids $Σ\subset \R^3$ which are strictly achiral. Since solenoids are non-planar, this contrasts sharply with the known fact that if there is a strictly achiral embedding $Y\subset \R^3$ of a compact polyhedron $Y$, then $Y$ must be planar.
format Preprint
id arxiv_https___arxiv_org_abs_math_0611900
institution arXiv
publishDate 2006
record_format arxiv
spellingShingle On tame embeddings of solenoids into 3-space
Jiang, Boju
Wang, Shicheng
Zheng, Hao
Zhou, Qing
Geometric Topology
Dynamical Systems
57N10, 37E99, 54C25
Solenoids are ``inverse limits'' of the circle, and the classical knot theory is the theory of tame embeddings of the circle into the 3-space. We give some general study, including certain classification results, of tame embeddings of solenoids into the 3-space as the ``inverse limits'' of the tame embeddings of the circle. Some applications are discussed. In particular, there are ``tamely'' embedded solenoids $Σ\subset \R^3$ which are strictly achiral. Since solenoids are non-planar, this contrasts sharply with the known fact that if there is a strictly achiral embedding $Y\subset \R^3$ of a compact polyhedron $Y$, then $Y$ must be planar.
title On tame embeddings of solenoids into 3-space
topic Geometric Topology
Dynamical Systems
57N10, 37E99, 54C25
url https://arxiv.org/abs/math/0611900